A Smoothing Newton Method for Extended Vertical Linear Complementarity Problems
A Smoothing Newton Method for Extended Vertical Linear Complementarity Problems
复制标题
DOI：
10.1137/s0895479897329837
复制
发表时间：
1999-10
期刊：
影响因子：
--
通讯作者：
H. Qi;L. Liao
中科院分区：
文献类型：
--
作者：
H. Qi;L. Liao
在本文中，我们将扩展垂直线性互补问题(EVLCP(m,q))重新表述为非光滑方程H(t,x)=0，其中$H: \mbox{\smallBbb R}^{n+1} \to \mbox{\smallBbb R}^{n+1}$，$t \in \mbox{\smallBbb R}$是参数变量，$x \in \mbox{\smallBbb R}$是原始变量。除了 t=0 的点 (t,x) 外，H 是连续可微的。此外，H 是强半光滑的。将 EVLCP(m, q) 重新表述为非光滑方程基于所谓的聚合（平滑）函数。因此，提出了一种牛顿型方法，该方法生成所有 tk > 0 的序列 {wk=(tk,xk)}。我们证明，在行${\cal W}_0$-性质的假设下，该序列的每个累加点都是EVLCP(M, q)的解。如果行 ${\cal W}$ 属性在解点成立，则收敛速度是二次的。还给出了有希望的数值结果。
In this paper, we reformulate the extended vertical linear complementarity problem (EVLCP(m,q)) as a nonsmooth equation H(t,x)=0, where $H: \mbox{\smallBbb R}^{n+1} \to \mbox{\smallBbb R}^{n+1}$, $t \in \mbox{\smallBbb R}$ is a parameter variable, and $x \in \mbox{\smallBbb R}$ is the original variable. H is continuously differentiable except at such points (t,x) with t=0. Furthermore H is strongly semismooth. The reformulation of EVLCP(m, q) as a nonsmooth equation is based on the so-called aggregation (smoothing) function. As a result, a Newton-type method is proposed which generates a sequence {wk=(tk,xk)} with all tk >0. We prove that every accumulation point of this sequence is a solution of EVLCP(M, q) under the assumption of row ${\cal W}_0$-property. If row ${\cal W}$-property holds at the solution point, then the convergence rate is quadratic. Promising numerical results are also presented.